Question: What do the following two equations represent? $x+y = 3$ $5x+5y = -1$
Explanation: Putting the first equation in $y = mx + b$ form gives: $x+y = 3$ $y = -x+3$ Putting the second equation in $y = mx + b$ form gives: $5x+5y = -1$ $5y = -5x-1$ $y = -1x - \dfrac{1}{5}$ The slopes are equal, and the y-intercepts are different, so the lines are parallel.